Home Page of Alberto Bressan

Position

Information:

• Office: room 201 McAllister Building
• Office phone: (814) 865 1667
• Fax: (814) 865 3735

Teaching and mentoring:

• Math 514 - Partial Differential Equations II. Syllabus.
• Notes on Sobolev spaces (pdf file, 42 pages) , (a revised version of a chapter in the Functional Analysis book).
• Lecture Notes on Functional Analysis and Linear PDEs (pdf file, 188 pages) , with 30 figures and 130 HW problems.

Publications and CV:

• My CV (pdf-file) and list of publications (pdf-file).

Books:

• Hyperbolic Systems of Conservation Laws. The One Dimensional Cauchy Problem (bookcover.html).
• Introduction to the Mathematical Theory of Control (bookcover.pdf), (Contents and Introduction.ps), (errata.pdf).

Most of my papers on hyperbolic conservation laws are available on the NTNU preprint server (Trondheim, Norway).

My recent papers on optimization and control theory are available on the IAC preprint server (Rome, Italy).

Areas of current research:

• Hyperbolic systems of conservation laws and nonlinear wave equations.
• Impulsive control of Lagrangian system. Stabilization and optimal control by means of active constraints.
• Nonlinear control, non-cooperative differential games.
• Differential inclusions, dynamic blocking problems.
• Optimization problems for traffic flow.

• 1 - A mixing problem
• 2 - A blocking problem

Slides of recent talks:

• Optima and equilibria for a model of traffic flow
  (pdf-file, 34 pages) (animation: Model 1) (animation: Model 2) (animation: instability of Nash equilibrium, Model 2)
• Dynamic blocking problems
  (pdf-file, 40 pages)
• Non cooperative differential games: a homotopy approach
  (pdf-file, 27 pages)
• Controlling Lagrangian systems by active constraints
  (pdf-file, 31 pages)
• A tutorial on hyperbolic systems of conservation laws in one space dimension
  I - Basic concepts (pdf-file, 27 pages)
  II - Solutions to the Cauchy problem (pdf-file, 35 pages)
  III - Uniqueness and continuous dependence (pdf-file, 25 pages)
  IV - Vanishing viscosity approximations (pdf-file, 33 pages)

Some survey papers and tutorials:

• Dynamic Blocking Problems
  A survey (2011).
  (pdf-file, 29 pages)
• Noncooperative differential games. A tutorial
  Notes for a Summer course, Padova 2010.
  (pdf-file, 81 pages)
• Hyperbolic conservation laws: an illustrated tutorial
  Notes for a summer course, Cetraro 2009.
  (pdf-file, 81 pages)
• Viscosity solutions of nonlinear hyperbolic systems
  Proceedings HYP2002, Pasadena.
  (pdf-file, 21 pages)
• Hyperbolic systems of conservation laws in one space dimension
  Proceedings International Congress of Mathematicians, Beijing 2002.
  (pdf-file)
• Symmetries and blow up patterns
  A short tutorial, SISSA 1999.
  (pdf-file, 17 pages)
• Viscosity solutions of Hamilton Jacobi equations and optimal control problems
  An illustrated tutorial. Original version: Trondheim, NTNU 2001. Revised: Shanghai Jiao Tong University, 2011.
  (pdf-file, 49 pages)
• Lecture Notes on the Center Manifold Theorem
  S.I.S.S.A., 2003.
  (pdf-file, 16 pages)
• Notes on the Boltzmann equation
  lecture notes for a summer course, S.I.S.S.A., 2005.
  (pdf-file, 28 pages)
• BV solutions to hyperbolic system by vanishing viscosity
  Lecture notes for a C.I.M.E. course, 2003.
  (pdf-file, 77 pages)
• Impulsive control of Lagrangian systems and locomotion in fluids
  (pdf-file, 34 pages)

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Some other papers, preprints:

• On differential systems with vector-valued impulsive control
  (with F.Rampazzo) (pdf-file, 16 pages)
• Extremal selections of multifunctions generating a continuous flow
  (with G.Crasta) (pdf-file, 17 pages)
• On discontinuous differential equations
  (with W.Shen) (pdf-file, 14 pages)
• Optimal control problems on stratified domains
  (with Y.Hong) (pdf-file, 19 pages)
• Differential inclusions and the control of forest fires
  (pdf-file, 27 pages)
• The minimum speed for a blocking problem on the half plane
  (with T.Wang) (pdf-file, 18 pages)
• Global optimality conditions for a dynamic blocking problem
  (with T.Wang) (pdf-file, 37 pages)
• From optimal control to non-cooperative differential games: a homotopy approach
  (pdf-file, 23 pages)
• Trajectories of a differential inclusion with state constraints
  (with G.Facchi) (pdf-file, 15 pages)
• Multidimensional graph completions and Cellina approximable multifunctions
  (with R.DeForest) (pdf-file, 25 pages)
• On the optimal strategy for an isotropic blocking problem
  (with T.Wang) (pdf-file, 22 pages)
• On the stability of the best reply map for noncooperative differential games
  (with Z.Wang) (pdf-file, 18 pages)
• Optima and equilibria for a model of traffic flow
  (with K.Han) (pdf-file, 35 pages)
• Nash equilibria for a model of traffic flow with several groups of drivers
  (with K.Han) (pdf-file, 20 pages)
• Variational analysis of Nash equilibria for a model of traffic flow
  (with C.J.Liu, W.Shen, and F.Yu) (pdf-file, 21 pages)
• Examples of nonclassical feedback control problems
  (with D.Wei) (pdf-file, 22 pages)
• Non-classical problems of optimal feedback control
  (with D.Wei) (pdf-file, 32 pages)